A rope drive parallel mechanism control method based on position and rope dual space synchronization

Abstract

A control method for a rope-driven parallel system based on position and rope dual-space synchronization belongs to the field of multi-rope parallel drive system control. This invention solves the problems of low control accuracy and poor control stability in existing multi-rope parallel control methods. The technical solution adopted by this invention is as follows: Step 1, establishing the deviation coupling error vector e of the lengths of n ropes in the rope space. crc Step 2: Design the deviation coupling error vector e of the end effector position component in position space. prc Step 3, based on e crc and e prc The deviation coupling error vector e under the design position and rope dual space pcrc Step 4: Based on e pcrc Construct a position and rope dual-space synchronization controller u pcrcc Step 5, based on u pcrcc Construct the final position and rope dual-space synchronization rope-driven parallel system controller u tc‑pcrcc The method of this invention can be applied to the control of rope-driven parallel systems.

Description

Technical Field

[0001] This invention belongs to the field of control of multi-rope parallel drive systems, and specifically relates to a control method for rope-driven parallel systems based on position and rope dual-space synchronization. Background Technology

[0002] Rope-driven parallel systems have promising applications in many industrial scenarios; however, precisely controlling the position and orientation of their end effectors is complex and difficult, which greatly limits the practical application of rope-driven parallel robots. Rope-driven parallel systems employ a parallel distributed configuration. Their working principle is as follows: the system indirectly controls the position and orientation of the end effector by controlling n independent motors to drive n independent ropes. The drive unit of the rope-driven parallel system uses multiple independent flexible ropes. Whether the length adjustments of these ropes are synchronized, and whether the ropes oscillate during the adjustment process, will affect the control accuracy of the end effector's position and orientation. Therefore, the synchronization of rope lengths in the rope space is a factor directly affecting the control accuracy and stability of the end effector. Furthermore, considering that each position point of the end effector consists of six components—X, Y, and Z axis coordinates and rotation angles around these axes—the control synchronization of each component in the end effector's position space will also affect the control accuracy and stability of the end effector. However, existing control methods do not simultaneously consider the synchronization of rope length in the rope space and the synchronization of position components in the position space, resulting in relatively low control accuracy and poor control stability. Therefore, controller design needs to fully integrate both aspects, improving the synchronization of rope space and position space to enhance the control effect on the end effector. Summary of the Invention

[0003] The purpose of this invention is to solve the problems of low control accuracy and poor control stability of existing multi-rope parallel control methods, and to propose a rope-driven parallel system control method based on position and rope dual-space synchronization.

[0004] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0005] A control method for a rope-driven parallel system based on position and rope dual-space synchronization, the method specifically includes the following steps:

[0006] Step 1: Establish the deviation coupling error vector e of the lengths of n ropes in rope space. crc ;

[0007] Step 2: Design the deviation coupling error vector e of the end effector position component in position space. prc ;

[0008] Step 3, based on ecrc and e prc The deviation coupling error vector e under the design position and rope dual space is... pcrc ;

[0009] Step 4, based on e pcrc Construct a position and rope dual-space synchronization controller u pcrcc ;

[0010] Step 5, based on u pcrcc Construct the final position and rope dual-space synchronization rope-driven parallel system controller u tc-pcrcc .

[0011] The beneficial effects of this invention are:

[0012] (1) This invention considers the influence of position spatial synchronization on the control process of the end effector and constructs a set of end effector position coupling error based on ring topology deviation coupling. The synchronous controller designed based on this coupling error can effectively improve the control stability and control accuracy of the end effector.

[0013] (2) Based on the constructed rope spatial deviation coupling error and position spatial deviation coupling error, a set of position and rope dual spatial deviation coupling errors is proposed. The synchronous controller designed based on this coupling error can effectively improve the synchronization of multi-rope length adjustment and the synchronization of end effector position and attitude adjustment.

[0014] (3) Based on the constructed position and rope dual-space deviation coupling error, this invention proposes a control framework for a rope-driven parallel system based on position and rope dual-space synchronization. Compared with traditional controllers, the controller designed using the framework of this invention can effectively improve the control accuracy of the end effector and reduce its own oscillation. Experimental results show that the controller designed using the method of this invention can reduce the X-axis tracking error by 77.8%, the Y-axis tracking error by 80.5%, and the Z-axis tracking error by 71.6%. Attached Figure Description

[0015] Figure 1 A comparison image of XY plane tracking for a figure-eight pattern;

[0016] Figure 2 This is a comparison chart of X-axis tracking errors;

[0017] Figure 3 A comparison chart of Y-axis tracking errors;

[0018] Figure 4 This is a comparison chart of Z-axis tracking errors. Detailed Implementation

[0019] The present application will now be described in further detail with reference to specific embodiments and accompanying drawings. Obviously, the described embodiments are merely a part of the embodiments of the present invention, and not all of them. Other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are all within the scope of protection of the present invention.

[0020] Specific Implementation Method 1: The rope-driven parallel system control method based on position and rope dual-space synchronization described in this implementation method specifically includes the following steps:

[0021] Step 1: Establish the deviation coupling error vector e of the lengths of n ropes in rope space. crc ;

[0022] Step 2: Design the deviation coupling error vector e of the end effector position component in position space. prc ;

[0023] Step 3, based on e crc and e prc The deviation coupling error vector e under the design position and rope dual space is... pcrc ;

[0024] Step 4, based on e pcrc Construct a position and rope dual-space synchronization controller u pcrcc ;

[0025] Step 5, based on u pcrcc Construct the final position and rope dual-space synchronization rope-driven parallel system controller u tc-pcrcc .

[0026] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the specific process of step one is as follows:

[0027] e crc =[e crc1 … e crcn ] T (1)

[0028] Among them, e crci Let be the deviation coupling error corresponding to the i-th rope, i = 1, 2, ..., n, where n is the number of ropes;

[0029] The deviation coupling error is defined using a ring topology as follows:

[0030]

[0031] Among them, l di e represents the expected length of the i-th rope. ciThe tracking error represents the length of the i-th rope.

[0032] The other steps and parameters are the same as in Specific Implementation Method 1.

[0033] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that the tracking error e of the length of the i-th rope is... ci for:

[0034] e ci =l i -l di (3)

[0035] Among them, l i Let be the actual length of the i-th rope.

[0036] Other steps and parameters are the same as in specific implementation method one or two.

[0037] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the specific process of step two is as follows:

[0038] e prc =[e prc1 … e prcn′ ] T (4)

[0039] Among them, e prci′ Let be the deviation coupling error corresponding to the i′th component in the motion vector X of the end effector, where i′ = 1, 2, ..., n′, and n′ is the number of components in the motion vector X;

[0040] Deviation coupling error e prci′ The ring topology is defined as follows:

[0041]

[0042] Among them, X di′ Let e ​​be the expected value corresponding to the i′-th component in the motion vector X. pi′ Let be the tracking error corresponding to the i′th component in the motion vector X.

[0043] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0044] For the case with 6 components, the motion vector X of the end effector is X = [b T Λ T ] T The displacement vector is b = [x o y o z o ] T The rotation vector is Λ=[αo β o γ o ] T .

[0045] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that the tracking error e corresponding to the i′th component in the motion vector X is... pi′ for:

[0046] e pi′ =X i′ -X di′ (6)

[0047] Among them, X i′ This is the actual value corresponding to the i′th component of the motion vector X.

[0048] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0049] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that the specific process of step three is as follows:

[0050] The deviation coupling vector e in rope space crc The deviation coupling error vector e in position space prc By performing weighted superposition, the deviation coupling error vector e in both position and rope dual-space is obtained. pcrc :

[0051] e pcrc =Je prc +e crc (7)

[0052] Where J is the Jacobian matrix.

[0053] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0054] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One to Six in that the specific process of step four is as follows:

[0055]

[0056] Among them, K pcp It is the proportional parameter matrix of PD control, K pcd It is the differential parameter matrix of PD control. It is the deviation coupling error vector e pcrc The derivative of .

[0057] K pcp =diag{K pcp1 ,K pcp2, ,…,Kpcpn}

[0058] K pcd =diag{K pcd1 ,K pcd2, ,…,K pcdn}

[0059] Among them, K pcpi For the proportional parameter matrix K pcp The i-th component, K pcdi For the differential parameter matrix K pcd The i-th component in K, where i = 1, 2, ..., n. pcpi and K pcdi You can set it according to the actual situation.

[0060] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0061] Specific Implementation Method Eight: This implementation method differs from Specific Implementation Methods One to Seven in that the specific process of step five is as follows:

[0062] u tc-pcrcc =u tc -u pcrcc (9)

[0063] Among them, u tc-pcrcc It is the final position and rope-driven parallel system controller for dual-space synchronization of rope, u tc It is a conventional controller.

[0064] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0065] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that the conventional controller u... tc It is a non-singular terminal sliding mode controller or a PID controller.

[0066] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0067] The conventional controller u in this embodiment tc It can be any modern control method, as long as the rope-driven parallel system is stable, including but not limited to non-singular terminal sliding mode controllers and PID controllers.

[0068] Example

[0069] The following example illustrates a specific implementation scheme using a rope-driven parallel robot controlled by three ropes, where three ropes control three free-moving robots. The complete dynamic model of the rope-driven parallel robot is shown in the following equation:

[0070]

[0071] Among them, I m Let R be the inertia matrix of the rope winding device. T This is the transmission ratio from the motor rotation angle to the rope length. For R T The inverse matrix of J, where J is the Jacobian matrix. T Let J be the transpose of J, and M be a positive definite symmetric inertia matrix. The translational acceleration vector of the end effector. F is the derivative of J. v The viscous friction matrix of the rope winding device. Let J be the translational velocity vector of the end effector. T ) + It is J T The left pseudo-inverse matrix of J can be calculated by the following formula: (J T ) + =(JJ T ) -1 J and G are gravity vectors, and u is the torque of the motor.

[0072] The following is an example of the application of a control method based on position and cable dual-space synchronization for the dynamic model shown in equation (10):

[0073] The first step is to design the deviation coupling error vector e in rope space. crc ;

[0074] e crc =[e crc1 e crc2 e crc3 ] T (11)

[0075] Among them, e crci (i = 1, 2, 3) represents the deviation coupling error corresponding to the i-th rope. This deviation coupling error adopts a loop topology structure, and its specific definition is as follows:

[0076]

[0077] Step 2: Design the deviation coupling error vector e in position space prc ;

[0078] e prc =[e prc1 e prc2 e prc3 ] T (13)

[0079] Among them, e prci(i = 1, 2, 3) represents the deviation coupling error corresponding to the i-th component of the motion vector X. This deviation coupling error adopts a ring topology structure, and its specific definition is as follows:

[0080]

[0081] Step 3: Design the deviation coupling error vector e in the dual space of position and rope. pcrc ;

[0082] e pcrc =Je prc +e crc (15)

[0083] Where J represents the Jacobian matrix;

[0084] Step 4: Construct a dual-space synchronization controller for position and rope. pcrcc ;

[0085]

[0086] Where K pcp and K pcd It is the parameter matrix of the position and rope dual-space synchronization controller, K pcp Let K be the scaling parameter matrix. pcd The differential parameter matrix;

[0087] Step 5: Construct the final position and rope-driven parallel system controller for dual-space synchronization. tc-pcrcc .

[0088] u tc A non-singular terminal sliding mode controller is selected, therefore u tc-pcrcc It can be obtained from the following formula:

[0089]

[0090] in, H eq =R T (J T ) + G, b d Let be the desired translation vector. Let e ​​be the desired translational acceleration vector. p =bb d =[e p1 e p2 e p3 ] T This represents the tracking error of the end effector position. For e p The first derivative, s, is based on the current error e.p The constructed sliding surface, Let K1 and K2 represent the 2-norm, β > 0, p and q are odd numbers greater than 0 and p > q, and K1 and K2 are both positive definite diagonal coefficient matrices.

[0091] To demonstrate the superiority of the rope-driven parallel system control method based on position and rope dual-space synchronization of the present invention, a comparative experiment will be conducted with a traditional APD controller, as follows:

[0092]

[0093] Among them, T exp Represents the expected tension of the rope. Represents the desired speed of the rope. e represents the expected acceleration of the rope. l This represents the error in rope length. K represents the rate of change of the error in rope length. p ,K d These are the parameters for the PD controller.

[0094] The relevant parameters selected in this comparative experiment are as follows:

[0095] K1=diag{10,10,10},K2=diag{1,1,1},K p =diag{35,35,35}, K d = diag{0.5,0.5,0.5}, K pcp =diag{13,22.1,22.1}, K pcd = diag{3.5, 2.65, 2.65}, R T =diag{0.063,0.063,0.063},F v =diag{0.6345,0.61711,0.62511}, G=[0,0,-3·9.8] T I m =diag{0.0536,0.0526,0.0526}, M=diag{3,3,3}, q=7, p=9, β=10.

[0096] The expected trajectory for this comparative experiment is: a flat circular trajectory: X8=-1+0.3·cos((1 / 10)πt), Y8=1+0.3·sin((1 / 5)πt), Z8=1.

[0097] Figure 1The image shows a comparison of the tracking of the figure-eight trajectory in the XY plane using two different control schemes. The dashed line represents the result of the comparison method (APD), while the solid line with stars represents the result of the method proposed in this invention (NTSM-PCRCC). Figures 2 to 4 The figures show a comparison of tracking errors along the X, Y, and Z axes. The dotted lines represent the results of the comparison method (APD), while the dashed lines represent the results of the method proposed in this invention (NTSM-PCRCC). As can be seen from the figures, the method proposed in this invention significantly improves the tracking accuracy of the desired trajectory, with a marked decrease in tracking errors along each axis. This demonstrates the effectiveness and superiority of the control method based on position and cable dual-space synchronization proposed in this invention.

[0098] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for controlling a rope-driven parallel mechanism based on position and rope dual spatial synchronization, characterized in that, The method specifically includes the following steps: Step 1: Establishing a rope space The deviation coupling error vector of the root rope length ; (1) in, For the first The deviation coupling error corresponding to each rope. , It refers to the number of ropes; The deviation coupling error is defined using a ring topology as follows: (2) in, Representing the The expected length of the rope, Representing the Tracking error of the rope length; Step 2: Design the deviation coupling error vector of the end effector position component in position space. ; Step 3, based on and Deviation coupling error vector in design position and rope dual space ; The specific process of step three is as follows: The deviation coupling vector in rope space The error vector coupled with the deviation in position space By performing weighted superposition, the deviation coupling error vector in both position and rope dual-space is obtained. : (7) in, It is a Jacobian matrix; Step 4, based on Construct a dual-space synchronization controller using position and rope. ; (8) in, It is the proportional parameter matrix of PD control. It is the differential parameter matrix of PD control. It is the deviation coupling error vector The derivative; Step 5, based on Construct the final position and rope dual-space synchronization rope-driven parallel system controller ; (9) in, It is a rope-driven parallel system controller that achieves final position and rope spatial synchronization. It is a conventional controller.

2. The control method for a rope-driven parallel system based on position and rope dual-space synchronization according to claim 1, characterized in that, The first Tracking error of rope length for: (3) in, For the first The actual length of the rope.

3. The control method for a rope-driven parallel system based on position and rope dual-space synchronization according to claim 2, characterized in that, The specific process of step two is as follows: (4) in, The motion vector of the end effector The Middle The deviation coupling error corresponding to each component , It is a motion vector The number of median components; Deviation coupling error The ring topology is defined as follows: (5) in, motion vector The Middle The expected value corresponding to each component motion vector The Middle The tracking error corresponding to each component.

4. The control method for a rope-driven parallel system based on position and rope dual-space synchronization according to claim 3, characterized in that, The motion vector The Middle The tracking error corresponding to each component for: (6) in, motion vector The The actual value corresponding to each component.

5. The control method for a rope-driven parallel system based on position and rope dual-space synchronization according to claim 4, characterized in that, The conventional controller It is a non-singular terminal sliding mode controller or a PID controller.

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